Computational complexity of tropical decomposition width

Determine the computational complexity of computing the tropical decomposition width of a tropical polynomial, including whether the problem is NP-hard or admits an efficient algorithm.

Background

The tropical decomposition width measures the minimum maximum degree among factors in a tropical polynomial decomposition. The paper develops structural and algorithmic consequences of this parameter but does not determine the complexity of computing it. A cited attempted NP-hardness proof is reported to contain errors, while related NP-hardness results do not resolve the width-computation problem.

References

What is the complexity of computing the tropical decomposition width of a tropical polynomial? attempted to prove NP-hardness, but their proof contains errors.

— On the Structure of $(\min,+)$ Convolution  (2608.13310 - Zhou, 13 Aug 2026) in Section titled “Open Problems”